Don't ever cut your own barrel (unless you have tens of thousands of dollars in equipment and know what your doing).
Just buy a short barreled upper. No paperwork needed. Buy one online from BCM and have it FedEx'd to your house the next day. Its not a firearm so there is no paperwork. Its the simplest and quickest part of the whole SBR process.
Its stupid I know - but welcome to the ATF.